Question

Explain why it does not matter which point you choose when writing the equation of the line in​ point-slope form, given two points.

Answer 1

In point-slope form, choosing different points to write the equation doesn't matter because any two distinct points uniquely determine the slope, ensuring consistency in the representation of the line.

In point-slope form, the equation of a line is
`\(y - y_1 = m(x - x_1)\)`, where
`\((x_1, y_1)\)` is a point on the line, and m is the slope. The choice of point doesn't matter because any two distinct points on a line uniquely determine its slope.

Regardless of the chosen point, substituting it into the formula yields the same equation.

This property makes the equation versatile, allowing flexibility in selecting points, while ensuring consistency in the representation of the line's slope and position.